Nonparametric Estimation of a Regression Function: Limiting Distribution2
- 28 June 1981
- journal article
- Published by Wiley in Australian Journal of Statistics
- Vol. 23 (2) , 186-195
- https://doi.org/10.1111/j.1467-842x.1981.tb00776.x
Abstract
Summary: Consider the regression modelYi= g(xi) + ei, i = 1,…, n, where g is an unknown function defined on [0, 1], 0 = x0< x1< … < xn≤ 1 are chosen so that max1≤i≤n(xi‐xi‐ 1) = 0(n‐1), and where {ei} are i.i.d. with Ee1= 0 and Var e1‐ s̀2. In a previous paper, Cheng & Lin (1979) study three estimators of g, namely, g1nof Cheng & Lin (1979), g2nof Clark (1977), and g3nof Priestley & Chao (1972). Consistency results are established and rates of strong uniform convergence are obtained. In the current investigation the limiting distribution of &in, i = 1, 2, 3, and that of the isotonic estimator g**nare considered.Keywords
This publication has 3 references indexed in Scilit:
- Non-Parametric Estimation of a Smooth Regression FunctionJournal of the Royal Statistical Society Series B: Statistical Methodology, 1977
- On the Nonparametric Estimation of Regression FunctionsJournal of the Royal Statistical Society Series B: Statistical Methodology, 1977
- Non-Parametric Function FittingJournal of the Royal Statistical Society Series B: Statistical Methodology, 1972